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Home Security Systems is analyzing the purchase of manufacturing equipment that will cost \(50,000. The annual cash inflows for the next three years will be:

Year

Cash flow

1

\)25,000

2

23,000

3

18,000

a. Determine the internal rate of return.

b. With a cost of capital of 18 percent, should the machine be purchased?

Short Answer

Expert verified
  1. Internal rate of return is 16.23%.
  2. The business entity must not purchase the machine.

Step by step solution

01

Definition Capital Budgeting

Capital budgeting is the method which include the discounting and non-discounting technique to determine whether to accept the any investment and project or not.

02

Internal rate of return

Averageofinflows=TotalofcashflowseachyearNumberofyears=$25,000+$23,000+$18,0003=$22,000

Calculation of PVIFA:

PVIFA=InitialinvestmentAveragecashflow=$50,000$22,000=2.273

For n=3, we will find 2.273 falls, around 15% or 16%.

Calculation of present value under each percent of estimated IRR:

15%:

Year

Cash flow

PVIF @ 15%

Present value

1

$25,000

0.869

$21,275

2

23,000

0.756

$17,388

3

18,000

0.665

$11,970

$50,633

16%:

Year

Cash flow

PVIF @ 16%

Present value

1

$25,000

0.862

$21,550

2

23,000

0.743

$17,089

3

18,000

0.641

$11,538

$50,177

Since NPV is still higher than the initial investment, we will try a higher rate:

Year

Cash flow

PVIF @ 17%

Present value

1

$25,000

0.855

$21,375

2

23,000

0.730

$16,790

3

18,000

0.624

$11,232

$49,397

The net present value is below the initial investment; the IRR will be between 16% and 17%. Now, We will interpolate:

Particular

Amount $

Present value of 16%

$50,177

Less: Present value of 17%

(49,397)

$780

Particular

Amount $

Present value of 16%

$50,177

Less: initial investment

(50,000)

$177

Calculation of IRR:

IRR=16%+$177$780=16%+0.23%=16.23%

03

Investment Decision

The business entity must not purchase the machine because the internal rate of return is less than the cost of capital.

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